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Full text of "Analytical Mechanics"

127.   Work. — The mechanical result produced by the action of a force in displacing a particle may be considered to be proportional to the interval of time during which the force acts or to the distance through which it moves.    In other words, we can take either the time or the displacement as the standard of measure.    The effect measured when the time is taken as the standard is different from that which is obtained when the displacement is made the standard. The first effect is called impulse.   It will be discussed in a later chapter.   The second is called work, the subject of this chapter.
128.   Measure of Work.—When a force moves a body it is said to do work.    The amount of work done equals the product of the force by the distance through which the -body is displaced along the line of action of the force.    In this definition the force is considered to be constant.    When it is variable the definition holds for infinitesimal displacements, since during the time taken by an infinitesimal displacement the force may be considered as constant.    Therefore if the particle P, Fig. 92, is displaced through ds,
under the action of the force F, the work done is
dW = F • ds cos a}
where a is the angle between the direc-tions of the force and the displacement. When the displacement is finite the work done equals the sum of the amounts of work done in